Option pricing with non-constant volatility

For the past three decades, researchers have developed models to price options with non-constant asset price volatility. These models can be divided into deterministic volatility models and stochastic volatility models. Deterministic volatility models assume that volatility is determined by some variables observable in the market. Stochastic volatility models suggest that volatility follows a stochastic process, whose parameters are not directly observable in the market. However, most of these authors have compared the results of their models with the classical Black-Scholes model [6], which assumes that volatility is constant. This dissertation investigates whether there is any model that can completely describe the market. Therefore, instead of com paring the results of the models with that of the Black-Scholes model, we have compared them with the market. For the purpose of this research, the S&P 500 Index option prices extracted from market are used. We investigate and compare for models: the GARCH(l ,I) model, the Constant Elasticity of Variance model, the Hull and White model, and the Heston model. The former two belong to deterministic volatility models and the latter two are stochastic volatility models. We conclude that none of the models under consideration can fully describe the market prices. Moreover, no model dominates the others by producing better results for all options.

Grantor dc:publisher.institution

Department of Mathematics and Applied Mathematics

Year dc:date.issued

2002

Author dc:creator

• Lin, Shih-Hsun

Advisor dc:contributor.advisor

• Ouwehand, Peter

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/11427/4902

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/4902